Table 1 Point estimators for the heterogeneity parameter
Point estimator for\({{\varvec{\tau}}}^{2}\) | Author (year) | Computation | Range | Assume normality | Estimation method | |
|---|---|---|---|---|---|---|
Cochran (Hedges-Olkin) | CA | Cochran (1954) [10] | Direct | Non-negative | No | Method of the moments |
Mandel-Paule | MP | Iterative | Non-negative | No | Method of the moments | |
DerSimonian-Laird | DL | DerSimonian & Laird (1986) [13] | Direct | Non-negative | No | Method of the moments |
Hartung-Makambi | HM | Hartung & Makambi (2002) [14] | Direct | Positive | No | Method of the moments |
Two-step Cochran | CA2 | DerSimonian & Kacker (2007) [15] | Direct | Non-negative | No | Method of the moments |
Two-step DerSimonian-Laird | DL2 | DerSimonian & Kacker (2007) [15] | Direct | Non-negative | No | Method of the moments |
Positive DerSimonian-Laird | DLp | Kontopantelis et al. (2013) [16] | Direct | Positive | No | Method of the moments |
Lin-Chu-Hodges r | LCHr | Lin et al. (2017) [17] | Iterative | Non-negative | No | Method of the moments |
Lin-Chu-Hodges m | LCHm | Lin et al. (2017) [17] | Iterative | Non-negative | No | Method of the moments |
Multistep DerSimonian-Laird | DLm | vanAert & Jackson (2018) [18] | Direct | Non-negative | No | Method of the moments |
Median-unbiased Mandel-Paule | MPM | Viechtbauer (2021) [19] | Iterative | Non-negative | No | Method of the moments |
Median-unbiased Gen. Q | GENQM | Viechtbauer (2021) [19] | Iterative | Non-negative | No | Method of the moments |
Maximum likelihood | ML | Hardy & Thompson (1996) [20] | Iterative | Non-negative | Yes | Maximum likelihood |
Restricted maximum likelihood | REML | Viechtbauer (2005) [21] | Iterative | Non-negative | Yes | Maximum likelihood |
Sidik-Jonkman | SJ | Sidik & Jonkman (2005) [22] | Direct | Non-negative | Yes | Least squares |
Sidik-Jonkman (prior CA estimation) | SJ(CA) | Sidik & Jonkman (2007) [23] | Direct | Positive | Yes | Least squares |
Non-parametric bootstrap DerSimonian-Laird | DLb | Kontopantelis et al. (2013) [16] | Direct | Non-negative | No | Non-parametric |
Malzahn-Böhning-Holling | MBH | Malzahn et al. (2000) [24] | Direct | Non-negative | No | Non-parametric |
Hunter-Schmidt (weighted by inversed variance) | HSiv | Hunter & Schmidt (1990) [25] | Direct | Non-negative | No | Artifact correction |
Hunter-Schmidt (weighted by sample size) | HSss | Hunter & Schmidt (1990) [25] | Direct | Non-negative | No | Artifact correction |
Hunter-Schmidt (corrected by small sample size) | HSk | Morris et al. (2015) [33] | Direct | Non-negative | No | Artifact correction |
Fully Bayesian | FB | Smith et al. (1995) [26] | Iterative | Non-negative | Yes | Bayesian |
Rukhin Bayes | RB | Rukhin (2013) [27] | Direct | Non-negative | No | Bayesian |
Rukhin Bayes positive | RBp | Rukhin (2013) [27] | Direct | Positive | No | Bayesian |
Bayes Modal | BM | Iterative | Positive | Yes | Bayesian |